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Operations and Algebraic Thinking Third Grade Fourth Grade Fifth Grade Analyze patterns and relationships. Write and interpret numerical expressions. Generate and analyze patterns. Gain familiarity with factors and multiples. Use the four operations with whole numbers to solve problems. Solve problems involving the four operations, and identify and explain patterns in arithmetic. Multiply and divide within 100. Understand properties of multiplication and the relationship between multiplication and division. Represent and solve problems involving multiplication and division. ______________________________________________________________________

3
Numbers and Operations in Base 10 Third Grade Fourth Grade Fifth Grade Perform operations with multi-digit whole numbers and with decimals to hundredths. Understand the place value system. Use place value understanding and properties of operations to perform multi-digit arithmetic. Generalize place value understanding for multi-digit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. ______________________________________________________________________

4
Numbers and Operations- Fractions Third Grade Fourth Grade Fifth Grade Develop understanding of fractions as numbers. Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand decimal notation for fractions, and compare decimal fractions. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Use equivalent fractions as a strategy to add and subtract fractions. ______________________________________________________________________

5
Measurement and Data Third Grade Convert like measurement units within a given measurement system. Fourth Grade Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Fifth Grade Represent and interpret data. Geometric measurement: understand concepts of angle and measure angles. Represent and interpret data Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Represent and interpret data. Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. ______________________________________________________________________

6
Geometry Third Grade Fourth Grade Fifth Grade Graph points on the coordinate plane to solve real-world and mathematical problems. Classify two- dimensional figures into categories based on their properties. Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Reason with shapes and their attributes. ______________________________________________________________________